“just as he spoke by the mouth of his holy prophets.” Zechariah understood actual prophecy, that it was God who was giving the words to speak to the prophets and thus God who spoke through the prophets. When a person prophesies through the power and inspiration of God, the prophet still has to cooperate with God. God does not possess and use the prophet as a musician uses an inanimate musical instrument. The prophet must cooperate with God and use his own mouth and voice as God supplies the words to the prophet's mind.
“from ancient times.” For this translation compare NJB and HCSB. The literal reading is “from of ages.” Hence, “from of old” would be a good alternative translation. In this case, from ancient times does not go back any further than David, because the prophets foretold that the Messiah would be from the house of David only during and after David’s lifetime (cp. Isa. 11:1).